Step-by-step explanation:
5 360
8 x
5x=360•8
x=576miles
The ages of three brothers are consecutive integers. The sum of their ages is 63. Find their ages.
How can you determine the number of solutions of a system of linear equations by inspecting its equations?
Step-by-step explanation:
To find - How can you determine the number of solutions of a system
of linear equations by inspecting its equations?
Proof -
There exists three types of solution for a system of linear equations.
1. No solution.
2. Unique solution.
3. Infinite many solutions.
Now,
Let the 2 linear equations are as follows :
y = ax + b
y = cx + d
1. For no solution -
a = c and b ≠d
For example-
y = -2x + 5
y = -2x - 1
Subtract first equation from second , we get
y - y = -2x - 1 - ( -2x + 5)
⇒0 = -2x - 1 + 2x - 5
⇒0 = -6
Not possible
So, There exist no solution.
2. For unique solution -
a ≠ c and b , d can be any value
For example -
If b and d are same ,
y = 2x - 4
y = -3x - 4
Subtract equation 1st from 2nd , we get
y - y = -3x - 4 - ( 2x - 4)
⇒0 = -3x - 4 - 2x + 4
⇒0 = -5x
⇒x = 0
⇒y = 2(0) - 4 = -4
∴ we get
x = 0, y = -4
If b and d are different
y = 2x - 4
y = -3x + 5
Subtract equation 1st from second
y - y = -3x + 5 - 2x + 4
⇒0 = -5x + 9
⇒-5x = -9
⇒x = [tex]\frac{9}{5}[/tex]
⇒y =2([tex]\frac{9}{5}[/tex]) - 4 = [tex]\frac{18}{5} - 4 = \frac{18 - 20}{5} = -\frac{2}{5}[/tex]
∴ we get
x = [tex]\frac{9}{5}[/tex] , y = [tex]-\frac{2}{5}[/tex]
3. Infinitely many solution -
a = c and b = d
For example -
y = -4x + 1
y = -4x + 1
Subtract equation first from equation second
y - y = -4x + 1 - ( -4x + 1)
⇒0 = -4x + 1 + 4x - 1
⇒0 = 0
Satisfied
So, Infinite many solution possible.
Q1 - Finding simple interest
Find the simple interest on a loan of:
£7500 borrowed for 6 years at a
rate of 12% p.a.
interest = £
Answer:
£ 5400
Step-by-step explanation:
P = £ 7500
r = 12% = 0.12
t = 6 years
Simple Interest = P*r*t
= 7500 * 0.12 * 6
= £ 5400
9) Find the value of two numbers if their sum is 17 and their difference is 1.
Answer: 9 and 8?
Step-by-step explanation:
find the value of given expression
[tex] \sqrt{312 \times 312} [/tex]
Step-by-step explanation:
[tex]
\sqrt{312 \times 312} \\ = \sqrt{312 ^{2} } \\ = 312
[/tex]
Hope it will help :)❤
Answer:
√{312×312}=√312²=±312 is your answer
Helppp im not very good at math so can you guys help me
Answer:
Answer is D. 75 cm2
Step-by-step explanation:
The closest estimate to 70.2 is 75 cm2
Hopefully this helps
What is the surface area of the square pyramid?
6 square meters
16 square meters
28 square meters
49 square meters
Answer:
16
Step-by-step explanation:
took the test
CAN SOMEONE HELP ME ASAP PLS I NEED TO SOLVE FOR DE
Answer:
c
Step-by-step explanation:
Terry has a box of craft beads.
• 11 are green
• 27 are yellow
• 24 are blue
• 38 are red
What percent of the beads are red?
Answer:
38% of the beads are red
3) The cost of a movie ticket and a candy bar is $5. The cost of 2 tickets
and a candy bar is $8.75. How much is a candy bar? *
Answer:
$1.25
Step-by-step explanation:
Given data
let the movie ticket be x and the candy bar be y
x+y= 5-------------1
also
2x+y= 8.75--------2
solve 1 and 2
x+y= 5
2x+y= 8.75
from 1
x= 5-y
put this inplace of x in 2
2(5-y)+y=8.75
10-2y+y= 8.75
10-y= 8.75
10-8.75=y
y= 1.25
Hence candy bar is $1.25
Put these fractions in order of size, smallest to largest.
7/10 2/3 4/5 11/15
Answer:
2/3,7/10,11/15,4/5
Step-by-step explanation:
You want to make them all have the same denominator so find a number all of the denominators can go to. In this case it seems to be 30.
7/10x3
21/30
2/3x10
20/30
4/5x6
24/30
11/15x2
22/30
Answer:
2/3, 7/10, 11/15, 4/5
Step-by-step explanation:
2/3= .66
7/10= .70
11/15=.73
4/5= .80
the decimals are numbers.
The product of 0.014 and 100,000 is
_ ...
because the decimal point in 0.014 moves
_ ...
places to the right.
Answer:
5
Step-by-step explanation:
In the case when we multiplied 0.014 by 100,000 so it comes
= 0.014 × 100,000
= 1,400
Since The value 0.014 were times by 5 zeros.
Therefore the decimal point would move 5 places to the right
Jacob has an $8 gift certificate to use
at a toy store. He decides to buy a toy
airplane that costs $8.61, and 3 toy
cars that cost $2.85 each.
If Jacob uses his gift certificate, how
much money will he need to pay?
A motorcycle drives 130 miles in 2 hours 36 minutes. Calculate the average speed.
Answer:
Average speed is like .83miles per minute and roughly 50 per hour
Step-by-step explanation:
(7^3)^-5
Please help! :)
What are the transformations on the following
function, f (x) = -2 log4 (x + 5) - 4?
Answer:
8
Step-by-step explanation:
= f (x) = -2 log 4 (x + 5) - 4
= 4 (-2 + 5) - 4
= So you do -2 + 5 because they are in ( ) so you do it first so (-2 + 5) = 3
= So now you have 4 (3) - 4
= You do 4 and (3) because when you have a 4 by a ( ) that means you multiply.
= 4 (3) which is the same as 4 × 3 which is 12.
= then you do 12 - 4 which is 8.
= 8 is your answer.
I hope this helps.
hi hi hi hi hi help help help help
Answer:
rate
Step-by-step explanation:
r(t)=d
r=d/t
r=miles/hour=mph
r=12
Answer: I THINK it’s d
Step-by-step explanation:
what is a median in a dot plot
Answer:
the median is the middle set of data.
Step-by-step explanation:
Fill in the blanks :)
Answer:
w+6=8 and w=2
Step-by-step explanation:
2(w+6) = 16
divide by two on both sides to remove the 2
w+6=16/2
w+6=8
-6 (remove six from both sides)
w=2
Match each shape (if possibles, and one at a time) using a translation of the original shape using a coordinate rule.
For the red figure: Translate 1 unit down then 3 units left, and for the blue figure: Reflect the figure at the y-axis.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
It is given that:
The figures are given in the picture:
For the red figure: Translate 1 unit down then 3 units left.
For the yellow figure: translate 5 units down and then 2 units right
For the blue figure: Reflect the figure at the y-axis.
Thus, for the red figure: Translate 1 unit down then 3 units left, and for the blue figure: Reflect the figure at the y-axis.
Learn more about the geometric transformation here:
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Someone help please? its late.
Answer:
It would be 10 units
you can use the midpoint formula.
Solve the inequality 18<-3(4x-2)
Answer:
Choice 1
Step-by-step explanation:
Answer:
x<-1 and Number 1
Step-by-step explanation:
:)
Find the surface area.
5 cm
14 cm
9 cm
3 cm
Answer:C. 2/3 cm/s
Step-by-step explanation:
Plz help me Jen can jump rope 80 times in 60 seconds. If she jumps at a constant ratio of seconds to jumps, how many jumps can she make in 15 seconds?
Answer:
The answer is 4
Step-by-step explanation:
You just divide 80 by 15.
She can jump rope 20 times in 15 seconds
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
/ Division operation: Divides left-hand operand by right-hand operand
For example 4/2 = 2
Given that Jen can jump rope 80 times in 60 seconds.
We have to determine the number of jumps can she make in 15 seconds.
Let the number of jumps would be x she can make in 15 seconds
Since she jumps at a constant ratio of seconds to jumps
So according to proportionality,
⇒ 80/60 = x/15
⇒ x = 15(80/60)
⇒ x = 20
Hence, she can jump rope 20 times in 15 seconds.
Learn more about the Ratio here:
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A glassblower can produce several sets of simple glasses in about 3 hours. When the glassblower works with
an apprentice, the job takes about 2 hours. Write an equation that can be used to find the amount of time t, in
hours, it would take for the apprentice to make the same number of sets of glasses when working alone.
Using the together rate, it is found that it would take the apprentice 6 hours to make the same number of sets of glasses when working alone.
What is the together rate?The together rate is the sum of each separate rate.
In this problem, the rates are:
Glassblower: 1/3.Apprentice: 1/x.Together: 1/2.Hence, applying the equation for the together rate:
[tex]\frac{1}{2} = \frac{1}{x} + \frac{1}{3}[/tex]
[tex]\frac{x + 3}{3x} = \frac{1}{2}[/tex]
[tex]2x + 6 = 3x[/tex]
[tex]x = 6[/tex]
It would take the apprentice 6 hours to make the same number of sets of glasses when working alone.
To learn more about the together rate, you can take a look at https://brainly.com/question/25159431
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
B.
Step-by-step explanation:
Tameka borrowed $300 to buy a digital music player she will pay the money back in 1 year at 5%simple interest how much money will tameka pay in interest
Answer:
$15 in interest
Step-by-step explanation:
sorry if it is wrong. I found 5% of 300 which is 15.
$15 money will tameka pay in interest.
What is interest?
Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
Here, we have,
formula: I = Prt.
here, we get,
given that,
Tameka borrowed $300 to buy a digital music player she will pay the money back in 1 year at 5%simple interest.
P=$300
r=5%
t=1year
so, I =$300*5%*1
=$15
Hence, $15 money will tameka pay in interest.
To learn more on interest click:
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what about these 2 ?
Answer:
11. A) 12
12. D)11
Step-by-step explanation:
11. We substitute x with 12 in 3(x)-11.
3(12)-11=
36-11= 25
We substitute x with 12 for the second equation (x+13).
12+13=25
Both answers match so the answer for #11 is 12.
12.We substitute x with 11 in 4(x)-4.
4(11)-4=
44-4=40
We substitute x with 11 for the second equation (2(x)+18)
2(11)+18=
22+18=40
Both answers match so the answer for #12 is 11.
Write an equation for the nth term of the arithmetic sequence
2,4,6,8,...
Step-by-step explanation:
dn means the difference (meaning what do you add/subtract to get the next number)
T0 means the term before the first one you got.
Tn = dn + T0
Tn = 2n + 0
Therefore our equation will be
Tn = 2n
Or in your case
An= 2n
find the value of x ?
Answer:x=33.6
Step-by-step explanation:
You would set up the equation 6/5 = x/28 Then you would cross multiply 6•28 then divide by 5
Answer:
Answer:33.6
Step-by-step explanation:
I just know it.